Study Committee B5 Colloquium
2005 September 14-16
Calgary, CANADA
316
Zero Sequence Current Compensation for Distance Protection applied to
Series Compensated Parallel Lines
TAKAHIRO KASE*
PHIL G BEAUMONT
Toshiba International (Europe) Ltd.
United Kingdom
SUMMARY
The effects of zero sequence mutual coupling on the performance of distance protection installed on
parallel transmission lines can be significant. It is well understood and documented that the effects of
mutual coupling can cause distance relays to over-reach or under-reach depending on the operational
status of the adjacent line. In principle, this problem can be solved by introducing the zero sequence
current from the parallel line to the relay on the faulted line. Nevertheless, manufacturers and users have
adopted a variety of coping strategies in order to compensate for these effects in cases where the adjacent
current is not available. However, recent experience has shown that there is another problem that must be
considered when distance relays are applied to series compensated parallel lines.
When a fault occurs on a series compensated transmission line, a transient oscillating current will flow
between the L and C components. This oscillation has a sub-synchronous frequency. Generally speaking, it
is difficult to remove the sub-synchronous frequency completely from the measured current and voltage,
hence the sub-synchronous components will affect distance measurement. In this paper, the undesirable
effect of mutual coupling on distance measurement is discussed theoretically together with practical
simulation cases and the benefit of introducing zero sequence compensation on parallel transmission lines
for distance calculation is also demonstrated using simulation studies.
Keywords: Distance relay – Series capacitor – Zero sequence compensation – Parallel line – Mutual
impedance – sub-synchronous frequency – EMTP – ATP
1. INTRODUCTION
Series compensated lines provide significant advantages in terms of improvements in power system
stability, an increase in the capacity of transmission lines etc. However, from a line protection perspective,
series compensated lines can cause many difficulties, particularly for distance protection relays. In order to
overcome problems numerous studies have been undertaken [1]-[4]. The main problems for distance
protections applied to compensated lines are overreach, directional element errors and oscillation of
impedance measurement. In previous studies, it has been recognized that problems occur in the case of
faults beyond the series capacitor. Therefore studies have focused on phenomena which were apparent for
*kaset@til.toshiba-global.com
316 - 1
faults occurring beyond the series capacitor and solutions have been proposed. In these studies, it would
appear that distance protections were able to calculate the impedance correctly for faults up to the series
capacitor.
Meanwhile, many studies in the application of distance relays to parallel lines have also been undertaken
[5], [6]. The main problem in the application of distance relays to parallel lines is the effect of the mutual
impedance of the parallel line on the phase-to-ground impedance measurement for earth faults.
Theoretically, it is apparent that the introduction of the residual current of the adjacent line is the easiest
and the most effective way of overcoming this problem. Many alternative methods have been proposed
because sometimes it is neither possible nor preferred to introduce the residual current of the adjacent line.
Our studies have revealed that the combination of parallel lines and series capacitors has caused new
problems for impedance measurement even when the fault occurs before the series capacitor. In this paper,
the new problems are introduced both theoretically and by simulation. It is shown that the introduction of
the residual current of the adjacent line is the solution to the problem.
2. MUTUAL ZERO SEQUENCE COMPENSATION
Firstly, the principle of distance measurement when distance protection is applied to parallel lines with
mutual impedance is shown in Fig.2.1 for a typical parallel line model with double end infeed.
P term
I0M
Q term
Z1, Z0
EP
～
EQ
ZP
VP
Z0M
IA ,I0
ZQ
VTs CTs
Z1F, Z0F
～
IF
Relay
Fig.2.1 Typical parallel line model with double end infeed
In Fig.2.1 it is assumed that an A-phase-to-ground fault occurs. The A phase voltage at the relay can then be
calculated as follows.
V PA = Z 1F I A + ( Z 0 F − Z 1F ) I 0 + Z MF I 0 M = Z 1 ( I A +
Z
Z 0 F − Z 1F
I 0 + 0 MF I 0 M )
Z 1F
Z 1F
(2.1)
= Z 1F ( I A + k s I 0 + k m I 0 M )
where,
VPA : A-phase voltage at P term, IA : A-phase current of faulted line
I0 : zero sequence current of faulted line, I0M : zero sequence current of adjacent line
Z1F : positive sequence impedance from relay to fault point
Z0F : zero sequence impedance from relay to fault point
Z0MF : zero sequence mutual impedance from relay to fault point
k s = ( Z 0 − Z1 ) / Z1 , k m = Z 0 M / Z 1
Therefore the impedance to the fault point can be calculated as follows.
Z 1F =
V PA
I A + k s I 0 + k m I 0M
(2.2)
If the zero-sequence current of the adjacent line is not available, distance relays must calculate the
impedance as follows.
Z '1F =
V PA
I A + ks I0
(2.3)
Examining (2.2) and (2.3), it is apparent that Z’1F is larger than Z1F when I0m is positive (i.e. in the same
316 - 2
direction) and that Z’1F is smaller than Z1F when I0m is negative (i.e. opposite direction). When faults occur
towards the far end of the line I0m is generally positive and distance relays may underreach. Overreach for
near faults is not so serious a problem for distance protection. Therefore one possible solution to this
problem is to use a larger value of ks than the calculated value. However, the direction of zero sequence
current can vary with the operational condition of the adjacent line, for example, the adjacent line may be
in operation or open or earthed. An alternative idea for adjusting the setting of ks is to introduce the status
of the adjacent line to the relay.
It is well known that the distance relay on the healthy line can overreach because of mutual zero sequence
compensation, and one solution to this problem is to block the mutual zero sequence compensation for
faults on the adjacent line. This can be detected by comparing the zero-sequence current of the protected
line to the zero-sequence current of the adjacent line. This solution has been applied for many years in
Japan.
3. SERIES COMPENSATED PARALLEL LINE
It is well recognized that faults beyond the series capacitor, as shown in Fig.3.1 cause two main problems
for distance measurement. The first problem is the overreach caused by the reduction in impedance by the
insertion of the capacitor in the line. The other problem is that sub-synchronous frequencies are
superimposed. This can be understood by solving the differential equation (3.1), and the fault current can
be given by (3.2) generally:-
E P sin ωt = Ri + L
di 1
+
idt
dt C ∫
(3.1)
I F = I m sin(ωt + φ ) + e −αt ( I m sin φ cosωC t + I n sin ωC t )
(3.2)
where,
ω : System angular velocity I m = EP / R 2 + (ωL − 1/ ωC ) 2 , α = R / 2L ,
2
2
ωC = 1/ LC − ( R / 2L) 2 , φ = tan −1 ( ωL − 1 / ωC ) , I n = − α + ωC I m cosφ + α I m sin φ
R
ω ⋅ ωC
ωC
Therefore the sub-synchronous frequency component, which is expressed by ωC, is superimposed on the
fundamental frequency component. Generally speaking, it is difficult to remove this frequency using a
digital filter, because the long data window required will cause a delay in operation. Hence the algorithm
for distance measurement must be immune to this lower frequency [7].
Fig.3.2 shows the parallel series compensated line model. In this model series capacitors are installed at
one end. It is clear that the zero-sequence current of the adjacent line will flow to the fault point through the
series capacitors for faults located up to the series capacitor. The influence of mutual impedance includes
the sub-synchronous frequency caused by the series capacitor. Furthermore the zero sequence current of the
adjacent line can be capacitive if the total capacitive reactance is larger than the line reactance. This
phenomenon is more likely to happen when the fault point is close to the series capacitor.
VTs CTs
R, L
P term
C
I0M
Q term
Z 1 , Z0
EP
EP
～
Relay
EQ
IF
～
～
EQ
SC
ZP
VP
Z0M
IA ,I0
ZQ
VTs CTs
xZ1, xZ0
Relay
IF
(1-x)Z1,
(1-x)Z0
～
SC
SC : series capacitance
0 ≤ x ≤1
Fig.3.1 Fault at series compensated line
Fig.3.2 Parallel series compensated line
316 - 3
xZ1
(1-x)Z1
xZ1
(1-x)Z1
2ZP1
C1
EP
C1
2ZQ1
EQ
～
～
EQ
positive-sequence 1st circuit
～
～
C1
EP
ZQ1
ZP1
(1-x)Z1
xZ1
xZ1
Relay
(1-x)Z1
C1
positive-sequence circuit
positive-sequence 2nd circuit
(1-x)Z2
xZ2
2ZP2
C2
xZ2
(1-x)Z2
C2
2ZQ2
ZQ2
ZP2
xZ2
(1-x)Z2
C2
negative-sequence 1st circuit
xZ2
Relay
(1-x)Z2
C2
negative-sequence circuit
negative-sequence 2nd circuit
xZ0
(1-x)Z0
C0
ZP0
2ZP0
xZ01
(1-x)Z01
C0
2ZQ0
ZQ0
xZ0
Z0M
(1-x)Z0
C0
zero-sequence 1st circuit
xZ00
Relay
(1-x)Z00
C0
zero-sequence circuit
zero-sequence 2nd circuit
Fig.3.3 Equivalent circuit using sequence
components
Fig.3.4 Equivalent circuit using sequence component
by 2-phase component method
Fig.3.3 shows the equivalent circuit using sequence components in the case of an A-phase-to-ground fault.
In Fig.3.3, the mutual impedance in the zero-sequence circuit complicates the calculation. It is well known
that by applying the 2-phase component method [8], the mutual impedance in the zero-sequence circuit can
be decoupled. The calculation method of conversion to 2-phase components is shown in (3.3) and the
method of re-conversion to normal sequence components is shown in (3.4). By means of the 2-phase
component method, Fig.3.3 is modified to Fig.3.4.
⎡V k1 ⎤ 1 ⎡1 1 ⎤ ⎡ Vk ,1L ⎤ ⎡ I k 1 ⎤ 1 ⎡1 1 ⎤ ⎡ I k ,1L ⎤
⎥, ⎢ ⎥ = ⎢
⎥
⎢V ⎥ = 2 ⎢1 − 1⎥ ⎢V
⎥⎢
⎦ ⎣ k , 2 L ⎦ ⎣ I k 2 ⎦ 2 ⎣1 − 1⎦ ⎣ I k , 2 L ⎦
⎣
⎣ k2 ⎦
(3.3)
⎡V k ,1L ⎤ ⎡1 1 ⎤ ⎡ V k1 ⎤ ⎡ I k ,1L ⎤ ⎡1 1 ⎤ ⎡ I k1 ⎤
(3.4)
⎢V
⎥=⎢
⎥=⎢
⎥, ⎢
⎥⎢
⎥⎢ ⎥
⎣ k , 2 L ⎦ ⎣1 − 1⎦ ⎣V k 2 ⎦ ⎣ I k , 2 L ⎦ ⎣1 − 1⎦ ⎣ I k 2 ⎦
where,
k=1, 2, 0 (positive, negative, zero sequence component respectively)
1, 2 : converted value of first circuit and second circuit respectively
1L, 2L : measured value of Line 1 and Line 2 respectively
For example, V02 is the zero sequence voltage of the second circuit shown in Fig.3.4 and I1,2L is
the positive sequence current of Line 2.
It should be noted that the mutual impedance is eliminated in Fig.3.4, and consequently it becomes easier to
see how the fault current flows. In Fig.3.4, Z00 and Z01 can be calculated as follows using the conversion
above.
Z 00 = Z 0 + Z 0 M , Z 01 = Z 0 − Z 0 M
(3.5)
The fault current flows to P-term side and Q-term side dependent on the ratio of the impedances of both
sides. The I0 of each line can be calculated as follows if If is assumed to be the total fault current, for
example:(3.6)
I 0,1L = I 01 + I 02 , I 0, 2 L = I 01 − I 02
where,
316 - 4
I 01 =
(1 − x) Z 0 + 2Z Q 0 − j (1 / ωC0 )
Z 0 + 2Z P 0 + 2Z Q 0 − j (1 / ωC0 )
(1 − x) Z 0 − j (1 / ωC 0 )
I f , I 02 =
If
Z 0 − j (1 / ωC 0 )
(3.7)
As described before, when the direction of I0,2L is different from the direction of I0,1L relays can overreach
when using (2.3) instead of (2.2) for impedance calculation. It is apparent that the relay would cause
overreach when the value of ‘x’ is close to 1, which means that the fault is near to the series capacitor. It can
also be seen that the phase angles of I0,2L and I0,1L can be different, and this difference causes phase errors
in the impedance measurement.
In addition to the above, it is clear that the sub-frequency component can vary between I0,1L and I0,2L.
Furthermore they can be different from Ia, which is calculated from I0+I1+I2. Therefore the sub-frequency
component can vary between “Ia+ksI0” and “Ia+ksI0+kmI0m”, which are the denominators of (2.2) and (2.3)
respectively, although their respective voltage is the same.
4. PRACTICAL SIMULATIONS AND ANALYSIS
Problems predicted in the application of distance protection to series compensated parallel lines have
been described theoretically in previous sections. In this section, simulations using EMTP/ATP have been
undertaken in order to understand the influence of mutual impedance. The model system used in the
simulation is shown in Fig.4.1. Parameters used in simulations are shown in Table 4.1.
SC
CTs
P-term
Z1,Z0
I0m
～
Q-term
MOV
～
Z0M
ZP1,ZP0
ZQ1,ZQ0
VTs
CTs
F0
F8
xZ1, xZ0
(1-x)Z1, (1-x)Z0
DZ
SC ZC
MOV
SC : Series Capacitors
MOV : Metal Oxide Varistors
Fig. 4.1 Simulation model
Table.4.1 Simulation parameters
Line impedance
[ohms]
Term-P source
Table.4.2 Fault points
Name
Value
Line length [km]
Voltage [kV]
Frequency [Hz]
200
275
50
10 + j76
40 + j184
30 + J84
j136
2+j72
j47
j37
-j46
Positive sequence impedance (Z1)
Zero sequence impedance (Z0)
Mutual zero sequence impedance (Z0M)
Positive sequence impedance (ZP1)
impedance
Zero sequence impedance (ZP0)
Term-Q source
Positive sequence impedance (ZQ1)
impedance [ohms]
Zero sequence impedance (ZQ0)
Series capacitor (ZC) [ohms]
Fault
point
Distance from A
reactance
x [%]
[ohms]
F0
0
0
F1
12.5
9.5
F2
25
19
F3
37.5
28.5
F4
50
38
F5
62.5
47.5
F6
75
57
F7
87.5
66.5
F8
100
76
Fault points checked in the simulations are shown in Table 4.2. From the results four cases have been
shown in this paper, (Figs. 4.2 to 4.5 inc.) with wave forms of I0 and I0m (the respective zero-sequence
currents of the protected and adjacent lines) together with the results of distance measurement. The figures
show the comparison between two methods of zero sequence compensation, one in which only the self
zero-sequence compensation is calculated using (2.3), and the other one in which the self and mutual
zero-sequence compensation is calculated using (2.2).
316 - 5
3000
3I0
3I0m
Current [A
2000
1000
0
0.10
-1000
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
-2000
-3000
Tim e [s]
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
-50.10
-10
Measured Reactance
Actual Reactance
Actual Resistance
Measured Resistance
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
-50.10
-10
Actual Reactance
Measured Reactance
Actual Resistance
Measured Resistance
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
Tim e [s]
Tim e [s]
Fig.4.2 Fault point F8(100%) (Upper: Waveform, Left: With mutual compensation, Right: Only self compensation)
Current [A
The following can be identified from Fig.4.2.
- The phase difference between I0 and I0m is almost 150 degrees.
- The impedance measurement using I0m and I0 is very stable and precise
- A significant oscillation and overreach by about 15% of impedance measurement can be seen for the case
where only I0 is used.
2000
1500
1000
500
0
-5000.10
-1000
-1500
-2000
-2500
3I0
3I0m
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
Tim e [s]
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
-50.10
-10
Reactance
Resistance
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
-50.10
-10
Reactance
Resistance
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
Tim e [s]
Tim e [s]
Fig.4.3 Fault point F6(75%) (Upper: Waveform, Left: With mutual compensation, Right: Only self compensation)
The following observations can be made upon examining Fig.4.3.
- The phase difference between I0 and I0m is almost 90 degrees.
- The impedance measurement using I0m and I0 is very stable and precise
- A significant oscillation whose amplitude is 10% of the theoretical impedance of impedance measurement
can be seen for the case where only I0 is used.
- Overreach of resistance measurement can be seen for the case using only I0, although the reactance
measurement is close to the theoretical value. This is the phase error in the impedance measurement.
316 - 6
3000
3I0
3I0m
Current [A
2000
1000
0
0.10
-1000
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
-2000
-3000
Tim e [s]
50
50
45
Reactance
45
Reactance
40
40
35
35
30
30
25
25
20
20
15
15
10
10
Resistance
5
0
0.10
-5
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
Resistance
5
0.30
0
0.10
-5
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
Tim e [s]
Tim e [s]
Fig.4.4 Fault point F4(50%) (Upper: Waveform, Left: With mutual compensation, Right: Only self compensation)
Current [A
The following can be identified from Fig.4.4.
- The phase difference between I0 and I0m is almost 60 degrees.
- The impedance measurement using I0m and I0 is very stable and precise
- A significant oscillation of impedance measurement can be seen for the case where only I0 is used.
- Underreach of reactance element and overreach of resistance measurement can be seen for the case where
only I0 is used.
4000
3000
2000
1000
0
-10000.10
-2000
-3000
-4000
-5000
3I0
3I0m
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
Tim e [s]
30
30
25
25
Reactance
20
15
15
10
10
Resistance
5
0
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
Reactance
20
Resistance
5
0.30
0
0.10
0.12
0.14
0.16
Tim e [s]
0.18
0.20
Tim e [s]
0.22
0.24
0.26
0.28
0.30
Fig.4.5 Fault point F2(25%) (Upper: Waveform, Left: With mutual compensation, Right: Only self compensation)
The following can be identified from Fig.4.5.
- The magnitude of I0m is almost zero, 100ms after the fault.
- The impedance measurement using I0m and I0 is very stable and precise
- The impedance measurement using only I0 is stable and precise
According to these results, it is expected that the following problems will be experienced in distance
measurement if I0m is not used in the calculation.
316 - 7
- The sub-synchronous frequency component can cause significant oscillations in distance measurement.
- Overreach for faults towards the far end of the line can occur due to the effect of mutual impedance,
which is not seen by the relay unless compensation for the parallel line is applied.
- The angular difference between I0 and I0m can be seen and can be considered as the reason for the error in
distance measurement.
- The effect of mutual impedance on distance measurement varies significantly with the fault point.
In order to compare the frequency components of the zero-sequence current in the protected line and the
adjacent line, the A-phase current, the denominator of (2.2) and (2.3) and the A-phase voltage, the results of
the FFTs(Fast Fourier Transform) of these waveforms are shown below. The data window is 100 ms from
fault inception. The fault point is F6, which is the same as that shown in Fig.4.3. The horizontal axis of the
following graph is f/f0, (f0 is the system frequency), and the vertical axis is the contribution of each
frequency component, in which the value of the basic frequency component is normalized to 1.
1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
2
4
6
8
0
10
0
Fig.4.6 Frequency diagram (I0)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
2
4
6
8
10
Fig.4.7 Frequency diagram (I0m)
8
10
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
Fig.4.8 Frequency diagram (Ia)
2
4
6
8
10
Fig.4.9 Frequency diagram (Ia+ksI0)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
Fig.4.10 Frequency diagram (Ia+ksI0+kmI0m)
0
2
4
6
8
10
Fig.4.11 Frequency diagram (Va)
On examining Figs. 4.6 to 4.10 inc., it can be seen that a large sub-synchronous component exists in I0
and I0m, compared to the sub-synchronous component which is smallest in (Ia+ksI0+kmI0m), the
compensated current. Hence, the introduction of the zero-sequence current of the adjacent line effectively
reduced the sub-synchronous component. If it is considered that the DC component in the current can be
316 - 8
eliminated almost completely by using a digital filter, it can be said that the frequency component in
“Ia+ksI0+kmI0m” is similar to that of the voltage. This fact can be considered as the main reason why the
introduction of the zero-sequence current of the adjacent line enables stable and precise distance
measurement.
5. CONCLUSION
This paper describes the problems associated with distance measurement when distance protection is
applied to series compensated parallel lines. The following points are confirmed both theoretically and by
practical simulation.
- Faults up to the series capacitor can cause problems such as oscillation, overreach for remote end faults
and phase error in distance measurement.
- These problems are caused by the mutual zero-sequence impedance. Sub-synchronous frequency
components in the zero-sequence current of the adjacent line cause oscillation in the measurement. The
angular difference between the zero-sequence current of the protected line and the zero-sequence current
of the adjacent line can cause overreach, underreach and phase error in the impedance measurement.
- The relationship between I0 and I0m varies with the fault point. This means that the effect of mutual zero
sequence impedance on distance measurement also varies with fault point.
- These problems can be solved completely by using mutual zero-sequence compensation by the
introduction of the zero-sequence current of the adjacent line.
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